Theory of charge nucleation in two dimensions

Thermal nucleation of two-dimensional charges is studied. It is argued that the probability of N charge pairs to appear has a simple asymptotics for large N: p(N)=[q(c,beta,mu)](N)/Z(beta,mu), where q(c,beta,mu) is a function of charge concentration c, inverse temperature beta, and chemical potential mu, and Z(beta,mu) is the partition function. We present q(c,beta,mu) as a limit value of some functional integral and find an approximate value of this limit. This provides thermodynamic description of nucleation transition. The probability distribution of charge positions is studied within the same approximation. The behavior of the probability distribution indicates that for small charge concentration the transition is of Kosterlitz-Thouless type, i.e., the dipoles nucleated dissociate and form a neutral plasma, while at larger charge concentration the transition corresponds to nucleation of dipoles that may remain bounded. A transition with respect to chemical potential is observed, for mu<mu(cr) the charge nucleation is a transition of infinite order, while for mu>mu(cr) it becomes a first-order transition.